10/19/2019
Colin Grudzien1,3, Marc Bocquet2 and Alberto Carrassi3,4
From: Carrassi, A. et al. Data assimilation in the geosciences: An overview of methods, issues, and perspectives. Wiley Interdisciplinary Reviews: Climate Change 9.5 (2018): e535.
From: Carrassi, A. et al. Data assimilation in the geosciences: An overview of methods, issues, and perspectives. Wiley Interdisciplinary Reviews: Climate Change 9.5 (2018): e535.
From: Carrassi, A. et al. Data assimilation in the geosciences: An overview of methods, issues, and perspectives. Wiley Interdisciplinary Reviews: Climate Change 9.5 (2018): e535.
From: Carrassi, A. et al. Data assimilation in the geosciences: An overview of methods, issues, and perspectives. Wiley Interdisciplinary Reviews: Climate Change 9.5 (2018): e535.
From: Carrassi, A. et al. Data assimilation in the geosciences: An overview of methods, issues, and perspectives. Wiley Interdisciplinary Reviews: Climate Change 9.5 (2018): e535.
From: Carrassi, A. et al. Data assimilation in the geosciences: An overview of methods, issues, and perspectives. Wiley Interdisciplinary Reviews: Climate Change 9.5 (2018): e535.
From: Carrassi, A. et al. Data assimilation in the geosciences: An overview of methods, issues, and perspectives. Wiley Interdisciplinary Reviews: Climate Change 9.5 (2018): e535.
An accurate representation of the true Bayesian posterior infeasible in geophysical models.
Therefore, the DA cycles typically estimates the first two moments of the posterior, or its mode.
The practical number of samples is typically on the order of \( \mathbf{\mathcal{O}\left(10^2\right)} \) due to the computational limits.
Courtesy of: Kaidor via Wikimedia Commons (CC 3.0)
From: Wilks, D. Effects of stochastic parametrizations in the Lorenz'96 system. Quarterly Journal of the Royal Meteorological Society 131.606 (2005): 389-407.
Two layer Lorenz-96 is used in benchmark twin experiments to study effects of model uncertainty and model reduction errors in multiscale dynamics;
In a deterministic, biased-model setting, the numerical precision the ensemble forecast can be substantially reduced without a major deterioration of the DA cycle's (relative) predictive performance2.
However, differences in statistical properties of model forecasts of stochastic dynamical systems have been observed due to the discretization errors of certain low-order schemes.
From: Grudzien et al. On the numerical integration of the Lorenz-96 model, with scalar additive noise, for benchmark twin experiments. Geoscientific Model Development. In submission.
From: Grudzien et al. On the numerical integration of the Lorenz-96 model, with scalar additive noise, for benchmark twin experiments. Geoscientific Model Development. In submission.
From: Grudzien et al. On the numerical integration of the Lorenz-96 model, with scalar additive noise, for benchmark twin experiments. Geoscientific Model Development. In submission.
From: Grudzien et al. On the numerical integration of the Lorenz-96 model, with scalar additive noise, for benchmark twin experiments. Geoscientific Model Development. In submission.
From: Grudzien et al. On the numerical integration of the Lorenz-96 model, with scalar additive noise, for benchmark twin experiments. Geoscientific Model Development. In submission.
From: Grudzien et al. On the numerical integration of the Lorenz-96 model, with scalar additive noise, for benchmark twin experiments. Geoscientific Model Development. In submission.
From: Grudzien et al. On the numerical integration of the Lorenz-96 model, with scalar additive noise, for benchmark twin experiments. Geoscientific Model Development. In submission.
From: Grudzien et al. On the numerical integration of the Lorenz-96 model, with scalar additive noise, for benchmark twin experiments. Geoscientific Model Development. In submission.
Typically, Lorenz-96 is simulated with a 4-stage Runge-Kutta scheme with step size up to \( 0.5 \) in deterministic settings.
We must distinguish between strong and weak convergence, and its impact on the truth-twin and the model-twin respectively.
Euler-Maruyama is a commonly used integration scheme for SDEs, but we find that it introduces strong, systematic bias into twin experiments when the step size is greater than or equal to \( \Delta=10^{-2} \).
We find that the 4-stage Runge-Kutta scheme is a statistically robust solver, without the systematic biases encountered in the Euler-Maruyama scheme.